In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of t...In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.展开更多
In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Gen...In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Generalized Orthogonal Matching Pursuit(GOMP)algorithms for solving this problem,we propose the Piecewise Generalized Orthogonal Matching Pursuit(PGOMP)algorithm,by considering the mixed-decaying sparse signals as piecewise sparse signals with two components containing nonzero entries with different decay factors.The algorithm incorporates piecewise selection and deletion to retain the most significant entries according to the sparsity of each component.We provide a theoretical analysis based on the mutual coherence of the measurement matrix and the decay factors of the nonzero entries,establishing a sufficient condition for the PGOMP algorithm to select at least two correct indices in each iteration.Numerical simulations and an image decomposition experiment demonstrate that the proposed algorithm significantly improves the support recovery probability by effectively matching piecewise sparsity with decay factors.展开更多
Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recov...Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.展开更多
We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algo...We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.展开更多
Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joi...Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model （JSM） 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with LI,2 recovery. Besides, with the help of the core concept of modified compressed sensing （CS） that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.展开更多
This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exa...This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.展开更多
For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based ...For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.展开更多
The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to e...The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.展开更多
When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To o...When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.展开更多
Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,...Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,and ultimately save the cost of equipment fault diagnosis in the aviation field.At present,the existing sparse decomposition methods generally extract sparse fault characteristics signals based on orthogonal basis atoms,which limits the adaptability of sparse decomposition.In this paper,a self-adaptive atom is extracted by the improved dual-channel tunable Q-factor wavelet transform(TQWT)method to construct a self-adaptive complete dictionary.Finally,the sparse signal is obtained by the orthogonal matching pursuit(OMP)algorithm.The atoms obtained by this method are more flexible,and are no longer constrained to an orthogonal basis to reflect the oscillation characteristics of signals.Therefore,the sparse signal can better extract the fault characteristics.The simulation and experimental results show that the selfadaptive dictionary with the atom extracted from the dual-channel TQWT has a stronger decomposition freedom and signal matching ability than orthogonal basis dictionaries,such as discrete cosine transform(DCT),discrete Hartley transform(DHT)and discrete wavelet transform(DWT).In addition,the sparse signal extracted by the self-adaptive complete dictionary can reflect the time-domain characteristics of the vibration signals,and can more accurately extract the bearing fault feature frequency.展开更多
In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for unde...In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.展开更多
A high resolution range profile(HRRP) is a summation vector of the sub-echoes of the target scattering points acquired by a wide-band radar.Generally, HRRPs obtained in a noncooperative complex electromagnetic environ...A high resolution range profile(HRRP) is a summation vector of the sub-echoes of the target scattering points acquired by a wide-band radar.Generally, HRRPs obtained in a noncooperative complex electromagnetic environment are contaminated by strong noise.Effective pre-processing of the HRRP data can greatly improve the accuracy of target recognition.In this paper, a denoising and reconstruction method for HRRP is proposed based on a Modified Sparse Auto-Encoder, which is a representative non-linear model.To better reconstruct the HRRP, a sparse constraint is added to the proposed model and the sparse coefficient is calculated based on the intrinsic dimension of HRRP.The denoising of the HRRP is performed by adding random noise to the input HRRP data during the training process and fine-tuning the weight matrix through singular-value decomposition.The results of simulations showed that the proposed method can both reconstruct the signal with fidelity and suppress noise effectively, significantly outperforming other methods, especially in low Signal-to-Noise Ratio conditions.展开更多
A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MO...A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.展开更多
Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with l...Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.展开更多
Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conven...Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.展开更多
We consider the problem of constructing one sparse signal from a few measurements. This problem has been extensively addressed in the literature, providing many sub-optimal methods that assure convergence to a locally...We consider the problem of constructing one sparse signal from a few measurements. This problem has been extensively addressed in the literature, providing many sub-optimal methods that assure convergence to a locally optimal solution under specific conditions. There are a few measurements associated with every signal, where the size of each measurement vector is less than the sparse signal＇s size. All of the sparse signals have the same unknown support. We generalize an existing algorithm for the recovery of one sparse signal from a single measurement to this problem and analyze its performances through simulations. We also compare the construction performance with other existing algorithms. Finally, the proposed method also shows advantages over the OMP （Orthogonal Matching Pursuit） algorithm in terms of the computational complexity.展开更多
The problem of two-dimensional direction finding is approached by using a multi-layer Lshaped array. The proposed method is based on two sequential sparse representations,fulfilling respectively the estimation of elev...The problem of two-dimensional direction finding is approached by using a multi-layer Lshaped array. The proposed method is based on two sequential sparse representations,fulfilling respectively the estimation of elevation angles,and azimuth angles. For the estimation of elevation angles,the weighted sub-array smoothing technique for perfect data decorrelation is used to produce a covariance vector suitable for exact sparse representation,related only to the elevation angles. The estimates of elevation angles are then obtained by sparse restoration associated with this elevation angle dependent covariance vector. The estimates of elevation angles are further incorporated with weighted sub-array smoothing to yield a second covariance vector for precise sparse representation related to both elevation angles,and azimuth angles. The estimates of azimuth angles,automatically paired with the estimates of elevation angles,are finally obtained by sparse restoration associated with this latter elevation-azimuth angle related covariance vector. Simulation results are included to illustrate the performance of the proposed method.展开更多
To improve the reconstruction performance of the greedy algorithm for sparse signals, an improved greedy algorithm, called sparsity estimation variable step-size matching pursuit, is proposed. Compared with state-of-t...To improve the reconstruction performance of the greedy algorithm for sparse signals, an improved greedy algorithm, called sparsity estimation variable step-size matching pursuit, is proposed. Compared with state-of-the-art greedy algorithms, the proposed algorithm incorporates the restricted isometry property and variable step-size, which is utilized for sparsity estimation and reduces the reconstruction time, respectively. Based on the sparsity estimation, the initial value including sparsity level and support set is computed at the beginning of the reconstruction, which provides preliminary sparsity information for signal reconstruction. Then, the residual and correlation are calculated according to the initial value and the support set is refined at the next iteration associated with variable step-size and backtracking. Finally, the correct support set is obtained when the halting condition is reached and the original signal is reconstructed accurately. The simulation results demonstrate that the proposed algorithm improves the recovery performance and considerably outperforms the existing algorithm in terms of the running time in sparse signal reconstruction.展开更多
It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical...It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.展开更多
The direction-of-arrival(DOA)estimation problem can be solved by the methods based on sparse Bayesian learning(SBL).To assure the accuracy,SBL needs massive amounts of snapshots which may lead to a huge computational ...The direction-of-arrival(DOA)estimation problem can be solved by the methods based on sparse Bayesian learning(SBL).To assure the accuracy,SBL needs massive amounts of snapshots which may lead to a huge computational workload.In order to reduce the snapshot number and computational complexity,a randomize-then-optimize(RTO)algorithm based DOA estimation method is proposed.The“learning”process for updating hyperparameters in SBL can be avoided by using the optimization and Metropolis-Hastings process in the RTO algorithm.To apply the RTO algorithm for a Laplace prior,a prior transformation technique is induced.To demonstrate the effectiveness of the proposed method,several simulations are proceeded,which verifies that the proposed method has better accuracy with 1 snapshot and shorter processing time than conventional compressive sensing(CS)based DOA methods.展开更多
基金supported by Natural Science Foundation of China(62071262)the K.C.Wong Magna Fund at Ningbo University.
文摘In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.
基金Supported by the National Key R&D Program of China(Grant No.2023YFA1009200)the National Natural Science Foundation of China(Grant Nos.12271079+1 种基金12494552)the Fundamental Research Funds for the Central Universities of China(Grant No.DUT24LAB127)。
文摘In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Generalized Orthogonal Matching Pursuit(GOMP)algorithms for solving this problem,we propose the Piecewise Generalized Orthogonal Matching Pursuit(PGOMP)algorithm,by considering the mixed-decaying sparse signals as piecewise sparse signals with two components containing nonzero entries with different decay factors.The algorithm incorporates piecewise selection and deletion to retain the most significant entries according to the sparsity of each component.We provide a theoretical analysis based on the mutual coherence of the measurement matrix and the decay factors of the nonzero entries,establishing a sufficient condition for the PGOMP algorithm to select at least two correct indices in each iteration.Numerical simulations and an image decomposition experiment demonstrate that the proposed algorithm significantly improves the support recovery probability by effectively matching piecewise sparsity with decay factors.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.
基金National Natural Science Foundation of China(Grant Nos. 11271050 and 11371183)
文摘We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.
基金supported by the National Natural Science Foundation of China(61201149)the 111 Project(B08004)the Fundamental Research Funds for the Central Universities
文摘Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model （JSM） 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with LI,2 recovery. Besides, with the help of the core concept of modified compressed sensing （CS） that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.
基金The authors are very grateful to the anonymous referees for their valuable comments and suggestions. We want to thank Mr. Liang Chen at Hunan University for many useful comments. This work was supported by the National Natural Science Foundation of China under Grant 11271117.
文摘This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.
基金supported by the National Natural Science Foundation of China(6150117661201399)+1 种基金the Education Department of Heilongjiang Province Science and Technology Research Projects(12541638)the Developing Key Laboratory of Sensing Technology and Systems in Cold Region of Heilongjiang Province and Ministry of Education,(Heilongjiang University),P.R.China(P201408)
文摘For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.
基金National Basic Research Program of China(2011CB707000)Innovative Research Group National Natural Science Foundation of China(60921001)
文摘The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.
基金supported by National Natural Science Foundation of China (Grant No. 71271078)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2009AA04Z414)Integration of Industry, Education and Research of Guangdong Province, and Ministry of Education of China (Grant No. 2009B090300312)
文摘When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.
基金This work was supported by the National Key R&D Program of China(Grant No.2018YFB1503103).
文摘Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,and ultimately save the cost of equipment fault diagnosis in the aviation field.At present,the existing sparse decomposition methods generally extract sparse fault characteristics signals based on orthogonal basis atoms,which limits the adaptability of sparse decomposition.In this paper,a self-adaptive atom is extracted by the improved dual-channel tunable Q-factor wavelet transform(TQWT)method to construct a self-adaptive complete dictionary.Finally,the sparse signal is obtained by the orthogonal matching pursuit(OMP)algorithm.The atoms obtained by this method are more flexible,and are no longer constrained to an orthogonal basis to reflect the oscillation characteristics of signals.Therefore,the sparse signal can better extract the fault characteristics.The simulation and experimental results show that the selfadaptive dictionary with the atom extracted from the dual-channel TQWT has a stronger decomposition freedom and signal matching ability than orthogonal basis dictionaries,such as discrete cosine transform(DCT),discrete Hartley transform(DHT)and discrete wavelet transform(DWT).In addition,the sparse signal extracted by the self-adaptive complete dictionary can reflect the time-domain characteristics of the vibration signals,and can more accurately extract the bearing fault feature frequency.
基金the Research Foundation for Doctoral Programs of Higher Education of China (Grant No.20060280003)the Shanghai Leading Academic Discipline Project (Grant No.T0102)
文摘In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.
基金co-supported by the National Natural Science Foundation of China(Nos.61671463,61471379,61790551 and 61102166)。
文摘A high resolution range profile(HRRP) is a summation vector of the sub-echoes of the target scattering points acquired by a wide-band radar.Generally, HRRPs obtained in a noncooperative complex electromagnetic environment are contaminated by strong noise.Effective pre-processing of the HRRP data can greatly improve the accuracy of target recognition.In this paper, a denoising and reconstruction method for HRRP is proposed based on a Modified Sparse Auto-Encoder, which is a representative non-linear model.To better reconstruct the HRRP, a sparse constraint is added to the proposed model and the sparse coefficient is calculated based on the intrinsic dimension of HRRP.The denoising of the HRRP is performed by adding random noise to the input HRRP data during the training process and fine-tuning the weight matrix through singular-value decomposition.The results of simulations showed that the proposed method can both reconstruct the signal with fidelity and suppress noise effectively, significantly outperforming other methods, especially in low Signal-to-Noise Ratio conditions.
基金supported by the National Natural Science Foundation of China(61907014,11871248,11701410,61901160)Youth Science Foundation of Henan Normal University(2019QK03).
文摘A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.
基金the National Natural Science Foundation of China(No.70901018)
文摘Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.
基金Supported by the National Natural Science Foundation of China(61501385)Science and Technology Planning Project of Sichuan Province,China(2016JY0242,2016GZ0210)Foundation of Southwest University of Science and Technology(15kftk02,15kffk01)
文摘Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.
文摘We consider the problem of constructing one sparse signal from a few measurements. This problem has been extensively addressed in the literature, providing many sub-optimal methods that assure convergence to a locally optimal solution under specific conditions. There are a few measurements associated with every signal, where the size of each measurement vector is less than the sparse signal＇s size. All of the sparse signals have the same unknown support. We generalize an existing algorithm for the recovery of one sparse signal from a single measurement to this problem and analyze its performances through simulations. We also compare the construction performance with other existing algorithms. Finally, the proposed method also shows advantages over the OMP （Orthogonal Matching Pursuit） algorithm in terms of the computational complexity.
基金Supported by the National Natural Science Foundation of China(61331019,61490691)
文摘The problem of two-dimensional direction finding is approached by using a multi-layer Lshaped array. The proposed method is based on two sequential sparse representations,fulfilling respectively the estimation of elevation angles,and azimuth angles. For the estimation of elevation angles,the weighted sub-array smoothing technique for perfect data decorrelation is used to produce a covariance vector suitable for exact sparse representation,related only to the elevation angles. The estimates of elevation angles are then obtained by sparse restoration associated with this elevation angle dependent covariance vector. The estimates of elevation angles are further incorporated with weighted sub-array smoothing to yield a second covariance vector for precise sparse representation related to both elevation angles,and azimuth angles. The estimates of azimuth angles,automatically paired with the estimates of elevation angles,are finally obtained by sparse restoration associated with this latter elevation-azimuth angle related covariance vector. Simulation results are included to illustrate the performance of the proposed method.
基金The National Basic Research Program of China(973Program)(No.2013CB329003)
文摘To improve the reconstruction performance of the greedy algorithm for sparse signals, an improved greedy algorithm, called sparsity estimation variable step-size matching pursuit, is proposed. Compared with state-of-the-art greedy algorithms, the proposed algorithm incorporates the restricted isometry property and variable step-size, which is utilized for sparsity estimation and reduces the reconstruction time, respectively. Based on the sparsity estimation, the initial value including sparsity level and support set is computed at the beginning of the reconstruction, which provides preliminary sparsity information for signal reconstruction. Then, the residual and correlation are calculated according to the initial value and the support set is refined at the next iteration associated with variable step-size and backtracking. Finally, the correct support set is obtained when the halting condition is reached and the original signal is reconstructed accurately. The simulation results demonstrate that the proposed algorithm improves the recovery performance and considerably outperforms the existing algorithm in terms of the running time in sparse signal reconstruction.
基金supported by the National Natural Science Foundation of China(61171127)
文摘It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.
基金This work was supported by the National Natural Science Foundation of China under Grants No.61871083 and No.61721001.
文摘The direction-of-arrival(DOA)estimation problem can be solved by the methods based on sparse Bayesian learning(SBL).To assure the accuracy,SBL needs massive amounts of snapshots which may lead to a huge computational workload.In order to reduce the snapshot number and computational complexity,a randomize-then-optimize(RTO)algorithm based DOA estimation method is proposed.The“learning”process for updating hyperparameters in SBL can be avoided by using the optimization and Metropolis-Hastings process in the RTO algorithm.To apply the RTO algorithm for a Laplace prior,a prior transformation technique is induced.To demonstrate the effectiveness of the proposed method,several simulations are proceeded,which verifies that the proposed method has better accuracy with 1 snapshot and shorter processing time than conventional compressive sensing(CS)based DOA methods.
